Statistical estimation for heteroscedastic transformation regression models

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  • Author: Qihua Wang and Xuan Wang
  • Date: 11 January 2019
  • Copyright: Image copyright of Patrick Rhodes

Consider a censored heteroscedastic transformation regression model where both the transformation function and the error distribution function are completely unknown. In a paper published in The Canadian Journal of Statistics, a method is developed to estimate the transformation function, the regression parameter vector, and the single index parameter vector of the variance function by establishing an expression for the transformation function and two estimating equations for both the parameter vectors. It is shown that the estimator of the transformation function converges weakly to a mean zero Gaussian process, and the parametric estimators are asymptotically normal.

The paper is available via the link below and the authors explain their findings in further detail below:

Analysis of censored data under heteroscedastic transformation regression models with unknown transformation function

Qihua Wang and Xuan Wang

The Canadian Journal of Statistics, Volume 46, Issue 2, June 2018, pages 233-245

DOI: https://doi.org/10.1002/cjs.11347

thumbnail image: Statistical estimation for heteroscedastic transformation regression models

For survival data where the survival time is subject to right censoring, there are numerous models and methods to study effect of covariates to find risk factors. The most popular models include cox proportional hazards model, the proportional odds models, additive hazard model, accelerated failure time model, linear transformation model and so on. Given a real dataset, we may try the above models to analyze it. However, dual to model restriction, the above models may not fit some datasets well. The authors proposed a more general transformation model, which includes the above model as special examples, under random censorship: heteroscedastic transformation regression model with unknown transformation function and unknown variance function.

The authors developed a method to estimate covariate effect on both regression and error variance as well as the unknown transformation function by establishing an expres-sion for the transformation function and two estimating equations for both the parameter vectors which describes the covariate effect. The asymptotic theories of all the estimators were established. Since the proposed model is more general than existing models, the estimation of covariate effect is more robust.

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